Rigorous methods for global optimization
Recent advances in global optimization
A Generalized Interval Arithmetic
Proceedings of the International Symposium on Interval Mathemantics
Parametric Linear System of Equations, Whose Elements are Nonlinear Functions
SCAN '06 Proceedings of the 12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
Solving linear systems whose input data are rational functions of interval parameters
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
A comparison of methods for solving parametric interval linear systems with general dependencies
NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
Enclosure for the solution set of parametric linear systems with non-affine dependencies
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
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Many real-life problems can be modelled by systems of linear equations or safely transformed to the linear case. When uncertain model parameters are introduced by intervals, then a parametric interval linear system must properly be solved to meet all possible scenarios and yield useful results. In general case, system coefficients are nonlinear functions of parameters. The Direct Method for solving such systems is proposed. Affine arithmetic is used to handle nonlinear dependencies. Some illustrative examples are solved and the results are compared to the literature data produced by other methods.